The following information below was obtained by using paired data consisting of
ID: 3226794 • Letter: T
Question
The following information below was obtained by using paired data consisting of weights (in lb) of 27 cars and their highway fuel consumption amounts (in mi/gal). yˆ = 50.2 .0574x, R2 = .649, x = 2300, y = 72.3 (Use = .03)
a) Interpret R2 in the context of the problem. Is this a good model? Explain.
b) What is the linear correlation coefficient?
c) Perform an appropriate significance test to determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.
d) Perform an appropriate significance test to determine whether there is sufficient evidence that the weight of a car is a good linear predicator for highway fuel consumption.
e) Based on your result from parts (c) and (d) predict the amount of fuel consumption for a car that weights 5000 Ib.
Explanation / Answer
a) R^2 = 0.649
the model explains 64.9 % of the variability of the response data around its mean.
b) linear correlation coefficient = sqrt(r^2) = sqrt(0.649) =0.805605
c)
TS = r *sqrt( (n-2)/(1 -r^2))
=0.805605*sqrt(25/(1-0.649)) as n = 27
=6.798899
since p-value is 0.00001
hence we reject the null hypothesis
and conclude that there is sufficient evidence to support the claim of a linear correlation between the two variables.
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